. Read, analyze, and answer the given involving normal curve.
1. A continuous random variable X is normally distributed with a mean of 56.3 and standard deviation of 7.2. Illustrate a normal curve and find its probability.
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Given : A continuous random variable X is normally distributed with a mean of 56.3 and standard deviation of 7.2.
P ( 34.7 < X < 63.5)
To Find : probability.
Solution:
Z score = ( Value - Mean) /SD
= ( 34.7 - 56.3) /7.2
= - 3
=> 0.0013 data below this
(63.5 - 56.3) /7.2
= 1
=> 0.8413 data below this
P ( 34.7 < X < 63.5) = 0.8413 - 0.0013
= 0.84
P ( 34.7 < X < 63.5) = 0.84
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